A two‐step accelerated Landweber‐type iteration regularization algorithm for sparse reconstruction of electrical impedance tomography

Abstract

The image reconstruction of conductivity distribution in electrical impedance tomography (EIT) is a seriously ill‐posed inverse problem, which is easily affected by measurement noise. In this paper, we present a two‐step Landweber‐type iteration method and its accelerated version for sparse reconstruction of Jacobian‐based EIT problem. We aim at reconstructing a finite number of simply and small inclusions embedded at the homogeneous background conductivity. The sparsity of the inclusions with respect to the spacial domain is a prior assumed. This method we propose here contains the two‐step line searches, corresponding to the Landweber step and the approximate Landweber step equipped with a novel step parameter, respectively. To validate the advantage of the proposed method, numerical simulations have been carried out. Also, qualitative and quantitative comparisons are conducted. The results show that the proposed method significantly reduces the number of iterations and computational time needed to match an appropriate stopping criterion, relative to the conventional (one‐step) Landweber method. The performed numerical simulations show that our method is promising.